1. Field of the Invention
The present invention relates generally to digital communication systems using quadrature modulation techniques. More specifically, the invention relates to a system and method for blind detection of carrier frequency offsets in such systems.
2. Description of the Prior Art
A digital communication system typically transmits information or data using a continuous frequency carrier with modulation techniques that vary its amplitude, frequency or phase. After modulation, the signal is transmitted over a communication medium. The communication media may be guided or unguided, comprising copper, optical fiber or air and is commonly referred to as the communication channel.
The information to be transmitted is input in the form of a bit stream which is mapped onto a predetermined constellation that defines the modulation scheme. The mapping of each bit as symbols is referred to as modulation.
Each symbol transmitted in a symbol duration represents a unique waveform. The symbol rate or simply the rate of the system is the rate at which symbols are transmitted over the communication channel. A prior art digital communication system is shown in FIG. 1. While the communication system shown in FIG. 1 shows a single communication link, those skilled in this art recognize that a plurality of multiple access protocols exist. Protocols such as frequency division multiple access (FDMA), time division multiple access (TDMA), carrier sense multiple access (CSMA), code division multiple access (CDMA) and many others allow access to the same communication channel for more than one user. These techniques can be mixed together creating hybrid varieties of multiple access schemes such as time division duplex (TDD). The type of access protocol chosen is independent of the modulation type.
One family of modulation techniques is known as quadrature modulation and is based on two distinct waveforms that are orthogonal to each other. If two waveforms are transmitted simultaneously and do not interfere with each other, they are orthogonal. Two waveforms generally used for quadrature modulation are sine and cosine waveforms at the same frequency. The waveforms are defined ass1(t)=A cos(2πfct)  Equation 1ands2(t)=A sin(2πfct)  Equation 2where fc is the carrier frequency of the modulated signal and A is the amplitude applied to both signals. The value of A is irrelevant to the operation of the system and is omitted in the discussion that follows. Each symbol in the modulation alphabet are linear combinations generated from the two basic waveforms and are of the form a1 cos(2πfct)+a2 sin(2πfct) where a1 and a2 are real numbers. The symbols can be represented as complex numbers, a1+ja2, where j is defined as j=√−1.
The waveforms of Equations 1 and 2 are the most common since all passband transmission systems, whether analog or digital, modulate the two waveforms with the original baseband data signal. Quadrature modulation schemes comprise various pulse amplitude modulation (PAM) schemes (where only one of the two basic waveforms is used), quadrature amplitude modulation (QAM) schemes, phase shift keying (PSK) modulation schemes, and others.
A prior art quadrature modulator is shown in FIG. 2. The modulator maps the input data as a pair of numbers {a1, a2} which belong to a set defined by the modulation alphabet. a1 represents the magnitude (scaling) of the first waveform and a2 represents the magnitude (scaling) of the second waveform. Each magnitude is modulated (i.e. multiplied) by the orthogonal waveforms. Each individual modulator accepts two signal inputs and forms an output signal at the carrier frequency.
A prior art quadrature demodulator is shown in FIG. 3. The demodulator generates sine and cosine waves at a carrier frequency [fc]fLO for demodulation. Ignoring channel effects, the received signal can be represented asr(t)=a1(t)cos(2πfct+φ0)+a2(t)sin(2πfct+φ0)  Equation 3where a1(t) represents the plurality of amplitudes modulated on waveform s1(t) as defined by Equation 1 and a2(t) represents the plurality of amplitudes modulated on waveform s2(t) as defined by Equation 2. φ is an arbitrary phase offset which occurs during transmission.
The cosine and sine demodulator signal components are defined as:
                                          r            c                    ⁡                      (            t            )                          =                                                            r                ⁡                                  (                  t                  )                                            *                        ⁢                          cos              ⁡                              (                                  2                  ⁢                  π                  ⁢                                                                          ⁢                                      f                    LO                                    ⁢                  t                                )                                              =                                                    1                2                            ⁢                              a                1                            ⁢                              cos                ⁡                                  (                                                                                    (                                                                              f                            c                                                    -                                                      f                            LO                                                                          )                                            ⁢                      t                                        +                                          ϕ                      0                                                        )                                                      +                                          1                2                            ⁢                              a                2                            ⁢                              sin                ⁡                                  (                                                                                    (                                                                              f                            c                                                    -                                                      f                            LO                                                                          )                                            ⁢                      t                                        +                                          ϕ                      0                                                        )                                                      +                                          1                2                            ⁢                              a                1                            ⁢                              cos                ⁡                                  (                                                                                    (                                                                              f                            c                                                    +                                                      f                            LO                                                                          )                                            ⁢                      t                                        +                                          ϕ                      0                                                        )                                                      +                                          1                2                            ⁢                              a                2                            ⁢                              sin                ⁡                                  (                                                                                    (                                                                              f                            c                                                    +                                                      f                            LO                                                                          )                                            ⁢                      t                                        +                                          ϕ                      0                                                        )                                                                                        Equation        ⁢                                  ⁢        4            and
                                          r            s                    ⁡                      (            t            )                          =                                                            r                ⁡                                  (                  t                  )                                            *                        ⁢                          sin              ⁡                              (                                  2                  ⁢                  π                  ⁢                                                                          ⁢                                      f                    LO                                    ⁢                  t                                )                                              =                                                    1                2                            ⁢                              a                2                            ⁢                              cos                ⁡                                  (                                                                                    (                                                                              f                            c                                                    -                                                      f                            LO                                                                          )                                            ⁢                      t                                        +                                          ϕ                      0                                                        )                                                      -                                          1                2                            ⁢                              a                1                            ⁢                              sin                ⁡                                  (                                                                                    (                                                                              f                            c                                                    -                                                      f                            LO                                                                          )                                            ⁢                      t                                        +                                          ϕ                      0                                                        )                                                      -                                          1                2                            ⁢                              a                2                            ⁢                              cos                ⁡                                  (                                                                                    (                                                                              f                            c                                                    +                                                      f                            LO                                                                          )                                            ⁢                      t                                        +                                          ϕ                      0                                                        )                                                      +                                          1                2                            ⁢                              a                1                            ⁢                              sin                ⁡                                  (                                                                                    (                                                                              f                            c                                                    +                                                      f                            LO                                                                          )                                            ⁢                      t                                        +                                          ϕ                      0                                                        )                                                                                        Equation        ⁢                                  ⁢        5            
The carrier frequency components, fc+fLO, are suppressed by the lowpass filters. The signals after filtering are:
                                          y            c                    ⁡                      (            t            )                          =                                            1              2                        ⁢                          a              1                        ⁢                          cos              ⁡                              (                                                                            (                                                                        f                          c                                                -                                                  f                          LO                                                                    )                                        ⁢                    t                                    +                                      ϕ                    0                                                  )                                              +                                    1              2                        ⁢                          a              2                        ⁢                          sin              ⁡                              (                                                                            (                                                                        f                          c                                                -                                                  f                          LO                                                                    )                                        ⁢                    t                                    +                                      ϕ                    0                                                  )                                                                        Equation        ⁢                                  ⁢        6            and
                                          y            s                    ⁡                      (            t            )                          =                                            1              2                        ⁢                          a              2                        ⁢                          cos              ⁡                              (                                                                            (                                                                        f                          c                                                -                                                  f                          LO                                                                    )                                        ⁢                    t                                    +                                      ϕ                    0                                                  )                                              -                                    1              2                        ⁢                          a              1                        ⁢                          sin              ⁡                              (                                                                            (                                                                        f                          c                                                -                                                  f                          LO                                                                    )                                        ⁢                    t                                    +                                      ϕ                    0                                                  )                                                                        Equation        ⁢                                  ⁢        7            
If the local oscillator frequency in Equations 6 and 7 is equal to the carrier frequency, fLO=fc, and the phase offset is equal to zero, φ0=0, the right hand sides of Equations 6 and 7 become ½a1(t) and ½a2(t) respectively. Therefore, to effect precise demodulation, the local oscillator must have the same frequency and phase as that of the carrier waveform. However, signal perturbations occurring during transmission as well as frequency alignment errors between the local oscillators of the transmitter and receiver manifest a difference between the carrier and local oscillator frequencies which is known as carrier offset. A phase difference between the carrier and local oscillator frequency is created as well. However, if the difference in frequencies is corrected, the difference in phase is simple to remedy. Phase correction is beyond the scope of the present disclosure.
Carrier frequency offset is defined as:Δf=fc−fLO.  Equation 8
To synchronize either parameter, the frequency and phase offsets need to be estimated. In prior art receivers, frequency offset estimation is performed after a significant amount of data processing. Without correcting offset first, the quality of downstream signal processing suffers.
“Estimation of Frequency Offset in Mobile Satellite Modems” by Cowley et al. International Mobile Satellite Conference, 16-18 Jun. 1993, pp. 417-422, discloses a circuit for determining a frequency offsets in mobile satellite applications. The frequency offset estimation uses a low pass filter, an Mth power block, a square fast Fourier transform block and a peak search block.
“A method for Course Frequency Acquisition for Nyquist Filtered MPSK” by Ahmed IEEE Transactions on Vehicular Technology, vol. 5, no. 4, 1 Nov. 1996, pp. 720-731, discloses a frequency offset estimator for mobile satellite communications. The estimator uses a low pass filter, a decimator, a fast Fourier transform block and a search algorithm.
“Carrier and Bit Synchronization in Data Communication—A tutorial Review” by Franks IEEE Transactions on Communications, US, IEEE Inc. New York, vol. COM-28, no. 8, 1 Aug. 1980, pp. 1107-1121, discloses carrier phase recovery circuits using elementary statistical properties and timing recovery based on maximum-likelihood estimation theory.
What is needed is a system and method of detecting and estimating carrier frequency offset before any data signal processing is performed.